Spring Semester 12-13
Akila Weerapana
LECTURE 12: Phase Diagram Analysis
I. INTRODUCTION
Todays lecture continues our discusses how to analyze the dynamics of a system of dierential
equations using phase diagrams.
We saw in the last lecture that some st
Spring Semester 12-13
Akila Weerapana
Lecture 7: The Solow Model
I. INTRODUCTION
Economic growth is by far the most important topic in economics. In the words of the Nobel
Prize winning economist Robert Lucas The consequences for human welfare involved i
Spring Semester 12-13
Akila Weerapana
LECTURE 11: Solving Systems of Dierential Equations
I. INTRODUCTION
In the last lecture we discussed how to calculate the eigenvalues and eigenvectors of a matrix.
When the eigenvectors of a matrix were linearly inde
Spring Semester 12-13
Akila Weerapana
Lecture 10: Eigenvalues and Eigenvectors
I. INTRODUCTION
In the next two lectures we delve deeper into topics in matrix algebra, dierence and dierential equations.
The topics we cover today include calculating two i
Spring Semester 12-13
Akila Weerapana
Lecture 8: Solving the Solow Model
I. OVERVIEW
In the last lecture we derived the equations for the Solow model with technology. We then
drew a Solow diagram in terms of capital per eective worker and showed that the
Spring Semester 12-13
Akila Weerapana
Lecture 6: Solving Linear Dierential Equations
I. INTRODUCTION
In a previous lecture, we discussed the general principle of the dynamic nature of most
macroeconomic variables. with values that change over time. We th
Spring Semester 12-13
Akila Weerapana
Lecture 9: Dynamics of the Solow Model
I. OVERVIEW
In the last lecture we linearized, and then solved the dierential equation underlying the
Solow model to derive the time paths of the endogenous variables away from
Spring Semester 12-13
Akila Weerapana
Supplement to Lecture 3: Basics of Linear Algebra
I. INTRODUCTION
The tools of matrix algebra play a really important role in solving the model and in doing
comparative statics. As you will see today, matrices presen
Spring Semester 12-13
Akila Weerapana
Lecture 3: Matrix Algebra and the IS-MP/AD-IA Model
I. OVERVIEW
In the last lecture, we laid out the basics of linear algebra: we dened what matrices are, described elementary operations such as transposition, additi
Spring Semester 12-13
Akila Weerapana
Lecture 5: Solving the AD-IA Model
I. OVERVIEW
In the last lecture, we discussed some of the key general principles of solving linear dierence
equations. We discussed two solution methods: the general method and the
Spring Semester 12-13
Akila Weerapana
Lecture 4: Solving Linear Dierence Equations
I. OVERVIEW
In the rst few lectures of this course we derived the IS-MP/AD-IA model of economic
uctuations. We showed how the IS-MP model could be represented using matrix
Spring Semester 12-13
Akila Weerapana
Lecture 13: Dynamic Optimization in Continuous Time
I. INTRODUCTION
Todays lecture looks at techniques for solving dynamic optimization problems in continuous
time.
We begin by reviewing a few key concepts from stat
Spring Semester 12-13
Akila Weerapana
Lecture 15: Comparative Statics Using The Ramsey Model
I. INTRODUCTION
In the last class, we derived the neo-classical growth model, also known as the Ramsey
model, which endogenized the consumption decision. We deri
Spring Semester 12-13
Akila Weerapana
Lecture 14: The Ramsey Model
I. INTRODUCTION
Now that we have covered the basic concepts of dynamic optimization in continuous time,
we move on to using those techniques to develop economic models. The rst model we f
Spring Semester 12-13
Akila Weerapana
Lecture 25: Time Consistency
I. OVERVIEW
In discussing dynamic optimization under uncertainty, one of the key ideas was that even if
an optimal plan was formed, the actual path that would be followed would be dierent
Spring Semester 12-13
Akila Weerapana
Lecture 24: VARs: Key Econometric Concepts
I. INTRODUCTION
We now switch gears a little bit and move away from very theoretical models to focusing on
more empirical techniques that are important in macroeconomics. Th
Spring Semester 12-13
Akila Weerapana
Lecture 23: The Diamond-Dybvig Model
I. OVERVIEW
In our discussion of key models in macroeconomics, we will focus on a classic model that was
the precursor to current models of nancial crises which are obviously of g
Spring Semester 12-13
Akila Weerapana
Lecture 21: The Beveridge Curve
I. INTRODUCTION
In the last lecture, we examined a model that formalized the important idea that involuntary
unemployment exists as an equilibrium outcome of the economy. In that model
Spring Semester 12-13
Akila Weerapana
Lecture 22: Comparative Statics in the Search Model
I. INTRODUCTION
In the last lecture, we distilled the Mortensen-Pissarides model down to three equations.
The rst two equations, which we interpreted as a labor dem
Spring Semester 12-13
Akila Weerapana
Lecture 20: The Mortensen-Pissarides Model
I. INTRODUCTION
We will pivot away from consumption theory and focus on a new topic: unemployment.
Unemployment is the macroeconomic variable that arguably has the most dire
Spring Semester 12-13
Akila Weerapana
LECTURE 18: Consumption Under Uncertainty
I. INTRODUCTION
In the last lecture we analyzed a very general model of consumption built on a dynamic
optimization framework, allowing for interest rates, discount factors,
Spring Semester 12-13
Akila Weerapana
LECTURE 19: Precautionary Saving
I. INTRODUCTION
In the last lecture we moved away from the basic framework of complete certainty over the
path of future income and looked at the dynamic optimization problem faced by
Spring Semester 12-13
Akila Weerapana
LECTURE 17: Consumption
I. INTRODUCTION
In the last lecture we discussed how to solve dynamic optimization problems in discrete time.
In todays class we use this technique to analyze consumption models. The standard
Spring Semester 12-13
Akila Weerapana
Lecture 16: Dynamic Optimization in Discrete Time
I. INTRODUCTION
We switch our focus to solving dynamic optimization problems in discrete time. As I said
before, we can think of reasons why some models are in discre
Spring Semester 12-13
Akila Weerapana
Lecture 1: Introduction to Models
I. INTRODUCTION
Economics 302 is a new, advanced level course in macroeconomic analysis. The focus of this
course will be on macroeconomic models and the mathematical tools needed to
Spring Semester 12-13
Akila Weerapana
Lecture 2: The IS-MP/AD-IA Model
I. INTRODUCTION
In the last class, we discussed the use of models in economics and focused on a four step
approach to models: deriving the equations of the model, identifying the exog
Fall Semester 07-08
Akila Weerapana
LECTURE 15: DIFFERENTIAL EQUATIONS
I. INTRODUCTION
The last two lectures covered theory and applications in the area of dierence equations.
The next two lectures will cover theory and applications in the area of dieren
Fall Semester 07-08
Akila Weerapana
LECTURE 18: Systems of Equations
I. INTRODUCTION
In the last lecture we discussed how to calculate the eigenvalues and eigenvectors of a matrix.
When the eigenvectors of a matrix were linearly independent, the matrix w
Fall Semester 07-08
Akila Weerapana
LECTURE 17: ADVANCED MATRIX ALGEBRA
I. INTRODUCTION
In the next two lectures we return to topics in matrix algebra. Even thought this may seem
strange, given that we have spent the last few weeks analyzing dierence and
Fall Semester 07-08
Akila Weerapana
LECTURE 18a: Formulaic Solutions to Systems of Equations
I. INTRODUCTION
This supplement to Lecture 18 develops a formula that you can use to solve systems of
dierence and dierential equations in a mechanistic fashion.